In industrial applications that involve relatively long rotating tubes, e.g. tubes which have a large length to diameter ratio, a problem has been encountered in the past due to the eccentricity between the inner and outer cylindrical surfaces of the tube. When such tubes are rotated at relatively high speeds, the eccentricity between the inner and outer cylindrical surfaces of the tube causes relatively high levels of vibration which adversely affects the operation of the machine above speeds where the vibrations occur. Although machining techniques are available for achieving a satisfactory degree of concentricity in short tubes, these techniques are not applicable to tubes whose length to diameter ratio exceeds 10, and accordingly, a need exists for a machining technique which is capable of substantially reducing the eccentricity between the inner and outer cylindrical surfaces in such long tubes.